Common Core State Standards DECONSTRUCTED. Booklet I: Kindergarten to Second Grade, Math FOR INTERNAL USE ONLY


 Valerie Collins
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1 Common Core State Standards DECONSTRUCTED Booklet I: Kindergarten to Second Grade, Math
2 How to use this booklet You cannot teach a Common Core Standard you must teach the skills inside of each standard. This booklet presents each Common Core Standard broken down into components: 1. The College & Career Anchor Standard Component, which determines the level of critical understanding expected for the standard 2. The Content Standard the actual Common Core Standard printed completely 3. The skills within the standard and their Learning Target. The Learning Target tells you how to teach and assess the skill. Join us for free webinars on how to use Deconstructed Standards, go to and click events for a schedule of webinars. What you ll encounter in the pages to come: Cluster: Groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. 2.NBT.2 Mathematical Practice (MP): The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. Cluster: Understand place value. Demonstration: Count within 1000 Demonstration: Skipcount by 5s to 1000 Demonstration: Skipcount by 10 s to 1000 Demonstration: Skipcount by 100s to 1000 Domain: Number and Operations in Base Ten Domain: Larger groups of related standards. Standards from different domains may sometimes be closely relate Deconstruction: The standards are deconstructed into concise statements about what the students need to know and be able to do. They are organized by Learning Targets to make it easier to choose the correct method of instruction and assessment. note: fluency standards are marked with an asterisk
3 Index Page Number K.CC.1 5 Count to 100 by ones and by tens. K.CC.2 5 Count forward beginning from a given number within the known sequence (instead of having to begin at 1) K.CC.3 5 Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). K.CC.4 6 Understand the relationship between numbers and quantities; connect counting to cardinality. a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. c. Understand that each successive number name refers to a quantity that is one larger. K.CC.5 6 Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects. K.CC.6 7 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies K.CC.7 7 Compare two numbers between 1 and 10 presented as written numerals. K.OA.1 8 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. K.OA.2 8 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.3 9 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1). K.OA.4 9 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. *K.OA.5 9 Fluently add and subtract within 5. K.NBT.1 10 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = ); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. *Fluency standards are marked with an asterisk
4 Index Page Number K.MD.1 10 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. K.MD.2 10 Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. K.MD.3 11 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. ( < or = 10) K.G.1 11 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. K.G.2 12 Correctly name shapes regardless of their orientations or overall size. K.G.3 12 Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ). K.G.4 12 Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes. (e.g., having sides of equal length). K.G.5 12 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.6 13 Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle?
5 Counting and Cardinality Cluster: Know number names and the count sequence K.CC.1: Count to 100 by ones and by tens. K.CC.2: Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3: Write numbers from 0 to 20. Represent a number of objects with a written numeral 020 (with 0 representing a count of no objects). K.CC.1 K.CC.2 K.CC.3 Cluster: Know number names and the count sequence Knowledge: Know numerals to Domain: Counting and Cardinality Demonstration: Count to 100 by ones starting at 0 Demonstration: Count to 100 by tens Cluster: Know number names and the count sequence Demonstration: Count forward verbally by ones Cluster: Know number names and the count sequence MP: Use appropriate tools strategically Demonstration: Write numbers 0 to 20 Domain: Counting and Cardinality Domain: Counting and Cardinality Demonstration: Write the number that represents a given number of objects from
6 Cluster: Count to tell the number of objects K.CC.4: Understand the relationship between numbers and quantities; connect counting to cardinality. K.CC.4 K.CC.5 a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. c. Understand that each successive number name refers to a quantity that is one larger. K.CC.5: Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 120, count out that many objects. Cluster: Count to tell the number of objects Domain: Counting and Cardinality Knowledge: Represent quantities using numbers and represent numbers using quantities Reasoning: Match each object with one and only one number name and each number with one and only one object Reasoning: Recognize the number of objects is the same regardless of their arrangement or the order in which they were counted Reasoning: Realize that the last number name said tells the number of objects counted Reasoning: Generalize that each successive number name refers to a quantity that is one larger Demonstration: Say the number names in order while matching each object with a number when counting objects Cluster: Count to tell the number Domain: Counting and Cardinality of objects MP: Use appropriate tools strategically Knowledge: Count up to 20 objects that have been arranged in a line, rectangular array, or circle Knowledge: Count as many as 10 items in a scattered configuration Reasoning: Match each object with one and only one number name and each number with one and only one object Reasoning: Conclude that the last number of the counted sequence signifies the quantity of the counted collection Demonstration: Count out 120 objects 6
7 Cluster: Compare numbers K.CC.6: Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. K.CC.7: Compare two numbers between 1 and 10 presented as written numerals. K.CC.6 K.CC.7 Cluster: Compare numbers Domain: Counting and Cardinality MP: Construct viable arguments and critique the reasoning of others Knowledge: Describe greater than, less than, or equal to Reasoning: Determine whether a group of 10 or fewer objects is greater than, less than, or equal to another group of 10 or fewer objects Cluster: Compare numbers Domain: Counting and Cardinality Knowledge: Know the quantity of each numeral 110 Reasoning: Compare written numbers to determine if they are greater than, less than, or equal to each other 7
8 Operations and Algebraic Thinking Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, (e.g. claps), acting out situations, verbal explanations, expressions, or equations. K.OA.2: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = and 5 = 4 + 1) K.OA.4: For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. *K.OA.5: Fluently add and subtract within 5. K.OA.1 K.OA.2 Cluster: Understand addition as putting together and adding to, and Domain: Operations and understand subtraction as taking Algebraic Thinking apart and taking from. Knowledge: Know adding is putting together parts to make the whole Knowledge: Know subtracting is taking apart or taking away from the whole to find the other part Knowledge: Know the symbols and the words for adding and subtracting Reasoning: Analyze an addition or subtraction problem to determine whether to put together or take apart Reasoning: Model an addition/subtraction problem given a reallife story Demonstration: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations Cluster: Understand addition as putting together and adding to, and Domain: Operations and understand subtraction as taking Algebraic Thinking apart and taking from. MP: Make sense of problems and persevere in solving them Knowledge: Add and subtract within 10 (maximum sum and minuend is 10) Reasoning: Use objects/drawings to represent an addition and subtraction word problem Demonstration: Solve addition and subtraction word problems within 10 *Fluency standards are marked with an asterisk 8
9 K.OA.3 K.OA.4 *K.OA.5 Cluster: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. Domain: Operations and Algebraic Thinking MP: Make sense of problems and persevere in solving them Knowledge: Solve addition number sentences within 10 Reasoning: Decompose numbers less than or equal to 10 into pairs in more than one way Demonstration: Record decomposition of a number within 10 by a drawing or writing an equation Cluster: Understand addition as putting together and adding to, and Domain: Operations and understand subtraction as taking Algebraic Thinking apart and taking from. Knowledge: Know that two numbers can be added together to make ten Reasoning: Using materials or representations, find the number that makes 10 when added to the given number for any number from 1 to 9, and record the answer using materials, representations, or equations Reasoning: Find the number that makes 10 when added to the given number for any number from 1 to 9 Demonstration: Record, by drawing or equation, the number that makes 10 when added to a given number from 1 to 9 Cluster: Understand addition as putting together and adding to, and Domain: Operations and understand subtraction as taking apart Algebraic Thinking and taking from. Demonstration: Fluently with speed and accuracy add and subtract within 5 9
10 Number and Operations in Base Ten Cluster: Work with numbers to gain foundations for place value. K.NBT.1: Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects and drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = ); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. K.NBT.1 Cluster: Work with numbers to gain foundations for place value. Measurement and Data Cluster: Describe and compare measurable attributes. Domain: Number and Operations in Base Ten Knowledge: Know that the numbers represent a quantity Reasoning: Understand that numbers are composed of 10 ones and one, two, three, four, five, six, seven, eight, or nine ones Demonstration: Represent compositions or decompositions of by a drawing or equation K.MD.1: Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. K.MD.2: Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. K.MD.1 K.MD.2 Cluster: Describe and compare measurable Domain: Measurement and Data attributes. Knowledge: Know that objects have measurable attributes and know what they are called, such as length and weight Knowledge: Describe an object using multiple attributes such as: width, height, length, weight, etc. Cluster: Describe and compare measurable Domain: Measurement and Data attributes. Knowledge: Know the meaning of a variety of attributes Knowledge: Know that two objects can be compared using a particular attribute Reasoning: Compare two objects and determine which has more or less of a measurable attribute Demonstrate: Describe the measurable attribute difference 10
11 Cluster: Classify objects and count the number of objects in each category. K.MD.3: Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. ( < or = 10). K.MD.3 Geometry Cluster: Classify objects and count the Domain: Measurement and Data number of objects in each category. MP: Make sense of problems and persevere in solving them Knowledge: Recognize nonmeasurable attributes such as shape, color Knowledge: Recognize measurable attributes such as length, weight, height Knowledge: Know what classify and sort mean Knowledge: Know that a category is the group that an object belongs to according to a particular, selected attribute Knowledge: Understand one to one correspondence with ten or less objects Reasoning: Sort objects into categories by particular attributes Demonstration: Count objects in a given group Demonstration: Sort objects into categories then determine the order by number of objects in each category (limit category counts to be less than or equal to ten) Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.1: Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. K.G.2: Correctly name shapes regardless of their orientations or overall size. K.G.3: Identify shapes as twodimensional (lying in a plane, flat ) or threedimensional ( solid ). K.G.1 Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, Domain: Geometry cylinders, and spheres). MP: Make sense of problems and persevere in solving them MP: Construct viable arguments and critique the reasoning of others Knowledge: Describe objects in the environment using shape words Knowledge: Use positional words such as above, below, beside, in front of, behind, and next to Reasoning: Determine the relative position of position of 2 or 3dimensional shapes within the environment, using the appropriate positional words to describe them 11
12 K.G.2 K.G.3 Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, Domain: Geometry cubes, cones, cylinders, and spheres). Knowledge: Recognize that size does not affect the name of the shape Knowledge: Recognize that orientation does not affect the name of the shape Demonstration: Name shapes, regardless of orientation or size Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, Domain: Geometry cubes, cones, cylinders, and spheres). Knowledge: Define the difference between two and threedimensional shapes Demonstration: Determine if an object is two or threedimensional Cluster: Analyze, compare, create, and compose shapes. Cluster: Analyze, compare, create, and Domain: Geometry compose shapes. MP: Construct viable arguments and critique the reasoning of others Knowledge: Identify attributes of shapes Reasoning: Describe attributes of a variety of two and threedimensional shapes Reasoning: Analyze and compare two and threedimensional shapes, in different sizes and orientations, describing their similarities, differences, and other attributes Cluster: Analyze, compare, create, and Domain: Geometry compose shapes. MP: Use appropriate tools strategically Knowledge: Identify basic shapes Knowledge: Recognize and identify basic shapes in the real world Demonstration: Draw shapes found in the environment Product: Construct shapes from components (e.g., sticks and clay balls) K.G.4: Analyze and compare two and threedimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length). K.G.5: Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.6: Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle? K.G.4 K.G.5 PRODUCT 12
13 K.G.6 Cluster: Analyze, compare, create, and compose shapes. Domain: Geometry Knowledge: Identify simple shapes (squares, triangles, rectangles, hexagons) Reasoning: Analyze how to put simple shapes together to compose a new or larger shape Demonstration: Compose a new or larger shape using more than one simple shape 13
14 Common Core State Standards DECONSTRUCTED First Grade, Math
15 Index Page Number 1.OA.1 17 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.2 17 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.3 18 Apply properties of operations as strategies to add and subtract. Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) 1.OA.4 18 Understand subtraction as an unknownaddend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. 1.OA.5 19 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). *1.OA.6 19 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13 4 = = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). 1.OA.7 20 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, = 2 + 5, = OA.8 20 Determine the unknown whole number in an addition or subtraction equation relating to three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 =? 3, =?. 1.NBT.1 21 Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1.NBT.2 21 Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones called a ten. b. The numbers from are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). *Fluency standards are marked with an asterisk
16 Index Page Number 1.NBT.3 22 Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 1.NBT.4 22 Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1.NBT.5 23 Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 1.NBT.6 23 Subtract multiples of 10 in the range from multiples of 10 in the range (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 1.MD.1 23 Order three objects by length; compare the lengths of two objects indirectly by using a third object. 1.MD.2 24 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of samesize length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 1.MD.3 24 Tell and write time in hours and halfhours using analog and digital clocks. 1.MD.4 24 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 1.G.1 25 Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 1.G.2 25 Compose twodimensional shapes (rectangles, squares, trapezoids, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. 1.G.3 25 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters, and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
17 Operations and Algebraic Thinking Cluster: Represent and solve problems involving addition and subtraction. 1.OA.1: Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.2: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.OA.1 1.OA.2 Cluster: Represent and solve problems involving addition and subtraction. Domain: Operations and Algebraic Thinking MP: Make sense of problems and persevere in solving them.. Knowledge: Use a symbol for an unknown number in an addition or subtraction problem within 20 Reasoning: Interpret situations to solve word problems with unknowns in all positions within 20 using addition and subtraction Reasoning: Determine appropriate representations for solving word problems involving different situations using addition and subtraction within 20 Demonstration: Solve word problems within 20 using addition and subtraction Cluster: Represent and solve problems involving Domain: Operations and addition and subtraction. Algebraic Thinking MP: Make sense of problems and persevere in solving them Knowledge: Know how to add three whole numbers whose sum is less than or equal to 20 Demonstration: Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20 17
18 Cluster: Understand and apply properties of operations and the relationship between addition and subtraction. 1.OA.3: Apply properties of operations as strategies to add and subtract. Examples: If = 11 is known, then = 11 is also known. (Commutative property of addition.) To add , the second two numbers can be added to make a ten, so = = 12. (Associative property of addition.) 1.OA.4: Understand subtraction as an unknownaddend problem. For example, subtract 10 8 by finding the number that makes 10 when added to 8. 1.OA.3 1.OA.4 Cluster: Understand and apply properties of Domain: Operations and operations and the relationship between Algebraic Thinking addition and subtraction. Knowledge: Define properties of operation strategies Demonstration: Apply properties of operation as strategies to solve addition and subtraction problems Cluster: Understand and apply properties of Domain: Operations and operations and the relationship between Algebraic Thinking addition and subtraction. Knowledge: Identify the unknown in a subtraction problem Reasoning: Solve subtraction problems to find the missing addend Reasoning: Explain the relationship of addition and subtraction 18
19 Cluster: Add and subtract within OA.5: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2). *1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., = = = 14); decomposing a number leading to a ten (e.g., 13 4 = = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding by creating the known equivalent = = 13). 1.OA.5 *1.OA.6 Cluster: Add and subtract within 20. MP: Look for and express regularity in repeated reasoning Domain: Operations and Algebraic Thinking Knowledge: Know how to count on and count back Reasoning: Explain how counting on and counting back relate to addition and subtraction. Domain: Operations and Cluster: Add and subtract within 20. Algebraic Thinking Reasoning: Apply strategies to add and subtract within 20. Demonstration: Add fluently within 20 Demonstration: Subtract fluently within 20 *Fluency standards are marked with an asterisk 19
20 Cluster: Work with addition and subtraction equations. 1.OA.7: Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, = 2 + 5, = OA.8: Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 =? 3, =?. 1.OA.7 1.OA.8 Cluster: Work with addition and subtraction Domain: Operations and equations. Algebraic Thinking Knowledge: Explain the meaning of an equal sign (the quantity on each side of the equality symbol is the same) Reasoning: Compare the values on each side of an equal sign Reasoning: Determine if an equation is true or false Cluster: Work with addition and subtraction equations. Domain: Operations and Algebraic Thinking MP: Make sense of problems and persevere in solving them Knowledge: Recognize partpartwhole relationships of addition and subtraction equations Reasoning: Determine the unknown whole number in an addition or subtraction equation with three whole numbers 20
21 Number and Operations in Base Ten Cluster: Extend the counting sequence. 1.NBT.1: Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. 1.NBT.1 1.NBT.2 Cluster: Extend the counting sequence. Domain: Number and Operations in Base Ten MP: Look for and express regularity in repeated reasoning Knowledge: Recall numbers and numerals up to 120 Reasoning: Represent a number of objects up to 120 with a written numeral Demonstration: Count to 120, starting at any number less than 120. Demonstration: Read and write numerals up to 120 Cluster: Understand place value. Domain: Number and Operations in Cluster: Understand place value. Base Ten MP: Look for and express regularity in repeated reasoning Knowledge: Explain what each digit of a twodigit number represents Knowledge: Define a bundle of 10 ones as a ten Reasoning: Represent numbers as composed of a ten and correct number of ones Reasoning: Represent the numbers 20, 30, 40, 50, 60, 70, 80, and 90 as composed of the correct number of tens 1.NBT.2: Understand that the two digits of a twodigit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones called a ten. b. The numbers from are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones). 1.NBT.3: Compare two twodigit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. 21
22 1.NBT.3 1.NBT.4 Cluster: Understand place value. Domain: Number and Operations in Base Ten Knowledge: Identify the value of each digit represented in a twodigit number Knowledge: Know what each symbol represents >, <, and = Reasoning: Compare two twodigit numbers based on meanings of the tens and ones digits Reasoning: Use >, =, and < symbols to record the results of comparisons Cluster: Use place value understanding Domain: Number and Operations in and properties of operations to Base Ten add and subtract. Knowledge: Identify the value of each digit of a number within 100 Knowledge: Decompose any number within one hundred into ten(s) and one(s) Reasoning: Choose an appropriate strategy for solving an addition problem within 100 Reasoning: Relate the chosen strategy (using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction) to a written method (equation) and explain the reasoning used Reasoning: Use composition and decomposition of tens when necessary to add within 100 Cluster: Use place value understanding and properties of operations to add and subtract. 1.NBT.4: Add within 100, including adding a twodigit number and a onedigit number, and adding a twodigit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding twodigit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. 1.NBT.5: Given a twodigit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used. 1.NBT.6: Subtract multiples of 10 in the range from multiples of 10 in the range (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. 22
23 1.NBT.5 1.NBT.6 Cluster: Use place value understanding and properties of operations to add and subtract. Domain: Number and Operations in Base Ten MP: Construct viable arguments and critique the reasoning of others Knowledge: Identify the value of each digit in a number within 100 Knowledge: Explain how to mentally find 10 more or 10 less than a given twodigit number Reasoning: Apply knowledge of place value to mentally add or subtract 10 to/from a given two digit number Cluster: Use place value Domain: Number and Operations in understanding and properties of Base Ten operations to add and subtract. Knowledge: Identify the value of each digit of a number within 100 Reasoning: Subtract multiples of 10 in the range of from multiples of 10 in the range of (positive or zero differences) Reasoning: Choose appropriate strategy (concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction) for solving subtraction problems with multiples of 10 Reasoning: Relate the chosen strategy to a written method (equation) and explain the reasoning used Measurement and Data Cluster: Measure lengths indirectly and by iterating length units. 1.MD.1 Cluster: Measure lengths indirectly and by iterating length units. Domain: Measurement and Data MP: Use appropriate tools strategically Knowledge: Identify the measurement known as the length of an object Knowledge: Directly compare the length of three objects Reasoning: Order three objects by length Reasoning: Compare the lengths of two objects indirectly by using a third object (e.g., if the length of object A is greater than the length of object B, and the length of object B is greater than the length of object C, then the length of object A is greater than the length of object C) 1.MD.1: Order three objects by length; compare the lengths of two objects indirectly by using a third object. 1.MD.2: Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of samesize length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. 23
24 1.MD.2 Cluster: Measure lengths indirectly and by iterating length units. Domain: Measurement and Data Knowledge: Know to use the same size nonstandard objects as repeating units Knowledge: Know that length can be measured with various units Reasoning: Compare a smaller unit of measurement to a larger object Reasoning: Determine the length of a measured object to be the number of smaller iterated or repeated objects that equal its length Demonstration: Compose the measurement of an object using nonstandard units (e.g., paper clips, unifix cubes, etc.) by laying the units of measurement end to end with no gaps or overlaps Cluster: Tell and write time. 1.MD.3: Tell and write time in hours and halfhours using analog and digital clocks. 1.MD.3 Cluster: Tell and write time. Domain: Measurement and Data MP: Use appropriate tools strategically Knowledge: Recognize that analog and digital clocks are objects that measure time Knowledge: Know hour hand and minute hand and distinguish between the two Reasoning: Determine where the minute hand must be when the time is to the hour (o clock) Reasoning: Determine where the minute hand must be when the time is to the halfhour (thirty) Demonstration: Tell and write the time to the hour and halfhour correctly using analog and digital clocks Cluster: Represent and interpret data. 1.MD.4 Cluster: Represent and interpret data. Domain: Measurement and Data MP: Make sense of problems and persevere in solving them Knowledge: Recognize different methods to organize data Knowledge: Recognize different methods to represent data Reasoning: Organize data with up to three categories Reasoning: Represent data with up to three categories Reasoning: Interpret data representation by asking and answering questions about the data. 1.MD.4: Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 24
25 Geometry Cluster: Reason with shapes and their attributes. 1.G.1: Distinguish between defining attributes (e.g., triangles are closed and threesided) versus nondefining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 1.G.2: Compose twodimensional shapes (rectangles, squares, triangles, trapezoids, halfcircles, and quartercircles) or threedimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. 1.G.3: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths and quarters, and use the phrases half of, fourth of and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. 1.G.1 1.G.2 Cluster: Reason with shapes and their attributes. Domain: Geometry MP: Make sense of problems and persevere in solving them MP: Construct viable arguments and critique the reasoning of others Knowledge: Identify defining and nondefining attributes of shapes Reasoning: Compare and contrast defining and nondefining attributes of shapes Demonstrate: Draw shapes to show defining attributes Product: Build shapes to show defining attributes Cluster: Reason with shapes and their Domain: Geometry attributes. MP: Make sense of problems and persevere in solving them MP: Use appropriate tools strategically Knowledge: Know that shapes can be decomposed to create composite shapes Knowledge: Describe properties of original, decomposed and composite shapes Reasoning: Determine how the original and created composite shapes are alike and different Product: Create composite shapes Product: Compose new shapes from a composite shape PRODUCT PRODUCT 25
26 1.G.3 Cluster: Reason with shapes and their attributes. Domain: Geometry MP: Make sense of problems and persevere in solving them MP: Construct viable arguments and critique the reasoning of others MP: Look for and express regularity in repeated reasoning Knowledge: Partition circles and squares into two and four equal shares Knowledge: Identify when shares are equal Knowledge: Describe equal shares using vocabulary: halves, fourths and quarters, half of, fourth of, and quarter of Knowledge: Describe the whole as two of two or four of equal shares Reasoning: Analyze that dividing a circle or rectangle into more equal pieces creates smaller shares 26
27 Common Core State Standards DECONSTRUCTED Second Grade, Math
28 Index Page Number 2.OA.1 30 Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. *2.OA.2 30 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers. 2.OA.3 31 Determine whether a groups of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.4 31 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 2.NBT.1 32 Understand that the three digits of a threedigit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens called a hundred. b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.2 32 Count within 1000; skipcount by 5s, 10s, and 100s. 2.NBT.3 32 Read and write numbers to 1000 using baseten numerals, number names, and expanded form. 2.NBT.4 33 Compare two threedigit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. *2.NBT.5 33 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.6 34 Add up to four twodigit numbers using strategies based on place value and properties of operations. 2.NBT.7 34 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting threedigit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.8 34 Mentally add 10 or 100 to a given number , and mentally subtract 10 or 100 from a given number NBT.9 34 Explain why addition and subtraction strategies work, using place value and the properties of operations. *Fluency standards are marked with an asterisk
29 Index Page Number 2.MD.1 35 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. 2.MD.2 35 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3 35 Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4 36 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. 2.MD.5 36 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.6 36 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,, and represent wholenumber sums and differences within 100 on a number line diagram. 2.MD.7 37 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.8 37 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? 2.MD.9 38 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in wholenumber units. 2.MD Draw a picture graph and a bar graph (with singleunit scale) to represent a data set with up to four categories. Solve simple puttogether, takeapart, and compare problems 4 using information presented in a bar graph. 2.G.1 39 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. 2.G.2 39 Partition a rectangle into rows and columns of samesize squares and count to find the total number of them. 2.G.3 39 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.
30 Operations and Algebraic Thinking Cluster: Represent and solve problems involving addition and subtraction. 2.OA.1: Use addition and subtraction within 100 to solve one and twostep word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 2.OA.1 Cluster: Represent and solve Domain: Operations and Algebraic problems involving addition Thinking and subtraction. MP: Make sense of problems and persevere in solving them Knowledge: Identify the unknown in an addition or subtraction word problem Reasoning: Determine the appropriate operations needed to solve addition and subtraction problems in situations including add to, take from, put together, take apart, and compare Demonstration: Use drawings or equations to represent one and twostep word problems Demonstration: Add and subtract within 100 to solve onestep word problems with unknowns in any positions Demonstration: Write an addition and subtraction equation with a symbol for the unknown Cluster: Add and subtract within 20. *2.OA.2: Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two onedigit numbers. *2.OA.2 Domain: Operations and Algebraic Cluster: Add and subtract within 20. Thinking Knowledge: Know mental strategies for addition and subtraction Knowledge: Know from memory all sums of two onedigit numbers Demonstration: Apply mental strategies to add and subtract fluently within 20 Demonstration: Fluently add and subtract within 20 *Fluency standards are marked with an asterisk 30
31 Cluster: Work with equal groups of objects to gain foundations for multiplication. 2.OA.3: Determine whether a groups of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.4: Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. 2.OA.3 2.OA.4 Cluster: Work with equal groups of Domain: Operations and Algebraic objects to gain foundations Thinking for multiplication. MP: Look for and express regularity in repeated reasoning Knowledge: Recognize that in groups of even numbers objects will pair up evenly Knowledge: Recognize that in groups of odd numbers objects will not pair up evenly Reasoning: Determine whether a group of objects is odd or even, using a variety of strategies Reasoning: Generalize the fact that all even numbers can be formed from the addition of 2 equal addends Demonstration: Count a group of objects up to 20 by 2s Demonstration: Write an equation to express a given even number as a sum of two equal addends Cluster: Work with equal groups of Domain: Operations and Algebraic objects to gain foundations Thinking for multiplication. MP: Look for and express regularity in repeated reasoning Reasoning: Generalize the fact that arrays can be written as repeated addition problems Demonstration: Solve repeated addition problems to find the number of objects using rectangular arrays Demonstration: Write an equation with repeated equal addends from an array 31
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